An element employed for the second-harmonic generation (SHG) is described, for example, in Electronics Letters, Vol. 25, (1989), PP. 731-732. Its operation is based on a quasi-phase matching method.
Referring to FIG. 1, quasi-phase matching will be described. FIG. 1 shows an waveguide-type SHG element. Titanium is diffused in stripes at the +C surface of LiNbO.sub.3 substrate 10, so that domain-reversal regions 12 are formed with a spatial period .LAMBDA.. An optical waveguide 14 is formed orthogonally to the domain-reversal regions 12 by a proton exchanging method (Li.sup.+ -H.sup.+ exchanging method).
In FIG. 1, a fundamental wave (angular frequency: .omega., wavelength: .lambda.(.omega.)) enters the SHG element. Then the fundamental wave propagates in the light waveguide 14. During propagation, energy of the fundamental wave is partially converted to a second-harmonic angular frequency: 2.omega., wavelength: .lambda.(2.omega.)).
If the SHG element did not have the domain-reversal regions 12, the maximum power of the second-harmonic would be obtained when the fundamental wave goes up to the coherence length l.sub.c according to the following equation (1). ##EQU1##
Wherein, Nn(2.omega.) is an effective guide index of the second-harmonic in the n-th propagation mode, and Nm(.omega.) is the index of the fundamental wave in the m-th propagation mode.
For example, the coherence length l.sub.c is approximately 1.7 .mu.m, when both propagation modes are 0-th (m=n=0), .lambda.(.omega.) is 830 nm, and thickness d of the light waveguide 14 is 1 .mu.m.
In this case, the second-harmonic has maximum power at the first 1.7 .mu.m in the waveguide 14, and has none at the next 1.7 .mu.m. That is, even though the fundamental wave is longer than l.sub.c, power of the second-harmonic does not exceed a certain quantity. This comes from an incomplete phase-matching between the fundamental wave and the second-harmonic.
A phase-mismatching .DELTA.k is obtained according to the following equation. ##EQU2##
In order to correct the phase-mismatching .DELTA.k, the domain reversal regions 12 are formed with the spatial period .LAMBDA.(=2 l.sub.c) as shown in FIG. 2. Thereby the power of the second-harmonic is approximately proportional to the square of the propagation length.
To correct .DELTA.k completely, the following equation (2) is indicated in Optics Communications Vol. 6, 1972, pp. 301-302. EQU N(2.omega.)-N(.omega.)-.lambda.(2.omega.)/.LAMBDA.=0 (2)
Thus, when the domain reversal regions 12 are formed so as to satisfy equation (2), although the phases don't match each other, the second harmonic has power proportional to the square of the SHG element's length L.
However, it is difficult to satisfy equation (2), since the effective guide indices N(2.omega.) and N(.omega.) depend on dimensions of the light waveguide 14. Accuracy of these dimensions and also of the spatial period .LAMBDA. are still insufficient nowadays.
A dye laser is considered for a light source in the Optics Communications article Although it has the ability to change wavelength, the complete apparatus is not of compact size.